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ons is considering producing a pilot for a comedy series in t television network. The network may decide to reject the se urchase the rights to the series for either one or two years. A ther produce the pilot and wait for the network's decision or t nd series to a competitor for $100,000. Hale's decision altern of dollars) are as follows: State of Nature 1 Year, $2 tive Reject, $1 2 Year -100 50 15 - d₂ 100 100 10 - the states of nature are P(s₁) = 0.20, P(s₂) = 0.30, and P( of $5000, an agency will review the plans for the comedy chances of a favorable network reaction to the series. Assur esult in a favorable (F) or an unfavorable (U) review and t are relevant: 0.69 P(S1|F) = 0.09 P(S1 | U) = 0.45 0.31 P(S2|F) = 0.26 P(S2| U) = 0.39 P(S3F) = 0.65 P($3|U) = 0.16

ons is considering producing a pilot for a comedy series in t television network. The network may decide to reject the se urchase the rights to the series for either one or two years. A ther produce the pilot and wait for the network's decision or t nd series to a competitor for $100,000. Hale's decision altern of dollars) are as follows: State of Nature 1 Year, $2 tive Reject, $1 2 Year -100 50 15 - d₂ 100 100 10 - the states of nature are P(s₁) = 0.20, P(s₂) = 0.30, and P( of $5000, an agency will review the plans for the comedy chances of a favorable network reaction to the series. Assur esult in a favorable (F) or an unfavorable (U) review and t are relevant: 0.69 P(S1|F) = 0.09 P(S1 | U) = 0.45 0.31 P(S2|F) = 0.26 P(S2| U) = 0.39 P(S3F) = 0.65 P($3|U) = 0.16

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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19. Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: State of Nature 1 Year, $2 Decision Alternative Reject, $1 2 Years, $3 Produce pilot, d₁ -100 50 150 Sell to competitor, d₂ 100 100 100 The probabilities for the states of nature are P(s₁) = 0.20, P(s₂) = 0.30, and P($3) = 0.50. For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the fol- lowing probabilities are relevant: P(F) = 0.69 P(S1F) = 0.09 P(S2|F) = 0.26 P(S1 | U) = 0.45 P(S2|U) = 0.39 P(U) = 0.31 P(S3F) = 0.65 P(S3 | U) = 0.16 a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the ex- pected value? C. What is the expected value of perfect information? d. What is Hale's optimal decision strategy assuming the agency's information is used? What is the expected value of the agency's information? e. f. Is the agency's information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?
Transcribed Image Text:19. Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: State of Nature 1 Year, $2 Decision Alternative Reject, $1 2 Years, $3 Produce pilot, d₁ -100 50 150 Sell to competitor, d₂ 100 100 100 The probabilities for the states of nature are P(s₁) = 0.20, P(s₂) = 0.30, and P($3) = 0.50. For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the fol- lowing probabilities are relevant: P(F) = 0.69 P(S1F) = 0.09 P(S2|F) = 0.26 P(S1 | U) = 0.45 P(S2|U) = 0.39 P(U) = 0.31 P(S3F) = 0.65 P(S3 | U) = 0.16 a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the ex- pected value? C. What is the expected value of perfect information? d. What is Hale's optimal decision strategy assuming the agency's information is used? What is the expected value of the agency's information? e. f. Is the agency's information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?
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